# SOLUTION: Sheila noted that if she took her apartment number and increased it by 6,the result was a perfect square. She also noticed that if she decreased her apartment number by 6, the resu

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 Question 44179: Sheila noted that if she took her apartment number and increased it by 6,the result was a perfect square. She also noticed that if she decreased her apartment number by 6, the result was the square root of that perfect square. What is the apartment number?Answer by stanbon(57967)   (Show Source): You can put this solution on YOUR website!Sheila noted that if she took her apartment number and increased it by 6,the result was a perfect square. She also noticed that if she decreased her apartment number by 6, the result was the square root of that perfect square. What is the apartment number? Let the apartment be "x". Then x+6=y^2 And x-6=y Substituting get: x+6=(x-6)^2 x+6=x^2-12x+36 x^2-13x+30=0 x=[13+sqrt(49)]/2 or x=[13-sqrt(49)]/2 x=10 or x=3 Only x=10 is a valid answer for your problem. Can you tell why? Cheers, Stan H.